A COUPLING OF MULTISCALE FINITE ELEMENT METHOD AND ISOGEOMETRIC ANALYSIS

In this paper, we propose to use modified B-splines spanned on several macroelements as a basis for building the multiscale finite element method (MsFEM) trail functions. The main benefit of our approach is that the calculations of a multiscale function are done in one step on the whole support, in contrast to standard MsFEM shape functions that are evaluated coarse element by element and require a cumbersome gluing. Selected numerical experiments for flow in porous media with periodic and random material properties distributions were performed to test our modified MsFEM with the new basis functions. We found that the method indeed improves standard MsFEM for fast oscillating material properties. We observed that the resonance effect, when the ratio of inclusion size and coarse mesh size approaches 1 (epsilon / H -> 1) can be reduced by increasing the order of B-splines.